Question 55006
Ignoring the fact that the 1st digit cannot be zero you have 
(7C2)(5C3)*8*8 = 13440 7-digit numbers with 2-3's and 3-8's and 
any of the other 8 digits in the last two places.
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But some of these numbers DO have zero as the 1st digit; how many??
This many: one way to choose the 1st digit
           then (6C2)(4C3)*8= 480 to fill in the next 6 places.
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Final Answer 13440-480 = 12960
Cheers,
Stan H.